MATH Q1. What is the formula for the area of a triangle?

Answer:

A = ½ × base × height

The height must be PERPENDICULAR to the base.

Also useful: Heron’s formula when all 3 sides are known.

💡 ACT often hides the height inside the triangle — draw it yourself if needed.

MATH Q2. What are the properties of a 30-60-90 triangle?

Answer:

Sides are in ratio: 1 : √3 : 2

If short leg = x:

• Long leg = x√3

• Hypotenuse = 2x

Angles: 30°, 60°, 90°

💡 Memorize both special triangles (30-60-90 and 45-45-90) — ACT tests them often.

MATH Q3. What is the equation of a line in slope-intercept form?

Answer:

y = mx + b

m = slope (rise/run)

b = y-intercept (where line crosses y-axis)

To find x-intercept, set y = 0 and solve.

💡 Standard form Ax + By = C can always be converted to y = mx + b.

MATH Q4. How do you find the average (arithmetic mean) of a set of numbers?

Answer:

Mean = Sum of all values ÷ Number of values

Example: Mean of 4, 7, 9, 10 = 30 ÷ 4 = 7.5

ACT trick: Sum = Mean × Number of values

💡 If the mean and count are given, find the missing value using Sum = Mean × n.

MATH Q5. What is the Pythagorean theorem and when does it apply?

Answer:

a² + b² = c²

Applies ONLY to right triangles.

c = hypotenuse (longest side, opposite 90°)

a, b = the two legs

Common triples: 3-4-5, 5-12-13, 8-15-17

💡 Pythagorean triples save time — recognize them instantly on the ACT.

SCI Q6. What is the difference between an independent and dependent variable?

Answer:

Independent variable: what the researcher CHANGES (the cause).

Dependent variable: what is MEASURED as a result (the effect).

Example: Testing fertilizer on plants → fertilizer = independent, plant height = dependent.

💡 ‘I change the Independent variable. I measure the Dependent variable.’

SCI Q7. What does ‘directly proportional’ mean in a scientific graph?

Answer:

Two variables are directly proportional when one increases and the other increases at a constant rate.

Graph: a straight line through the origin.

Formula: y = kx (k = constant of proportionality)

💡 Inversely proportional = one goes up, the other goes down. Graph is a curve.

SCI Q8. What is the difference between an atom and a molecule?

Answer:

Atom: the smallest unit of an element. Cannot be broken down chemically.

Molecule: two or more atoms bonded together.

Examples: O₂ (oxygen molecule), H₂O (water molecule), CO₂

💡 Elements on the periodic table are atoms. Compounds are molecules of different elements.

SCI Q9. What is the law of conservation of mass?

Answer:

Matter cannot be created or destroyed in a chemical reaction.

The total mass of reactants = total mass of products.

This is why chemical equations must be balanced.

💡 ACT Science may show unbalanced equations — always check both sides are equal.

SCI Q10. What is the difference between speed and velocity?

Answer:

Speed: how fast an object moves — magnitude only (scalar).

Speed = distance ÷ time

Velocity: speed WITH direction (vector).

Velocity = displacement ÷ time

Example: 60 mph north = velocity. 60 mph = speed.

💡 Acceleration = change in velocity ÷ time. Changing direction = changing velocity.

ENG Q11. What is a run-on sentence and how do you fix it?

Answer:

A run-on joins two independent clauses without proper punctuation.

Fixes:

1. Add a period (make two sentences)

2. Add a semicolon

3. Add a comma + FANBOYS conjunction

4. Add a subordinating conjunction

💡 A comma alone between two independent clauses = comma splice (also wrong on ACT).

ENG Q12. What is the difference between ‘who’ and ‘whom’?

Answer:

Who = subject (doing the action)

Whom = object (receiving the action)

Trick: Substitute ‘he/she’ or ‘him/her’

• If ‘he’ fits → use WHO

• If ‘him’ fits → use WHOM

Example: Who called? (He called ✓)

💡 ‘Whom’ often follows prepositions: to whom, for whom, with whom.

ENG Q13. When should you use an apostrophe to show possession?

Answer:

Singular noun: add ‘s → dog’s collar

Plural noun ending in s: add ‘ only → dogs’ collars

Plural noun NOT ending in s: add ‘s → children’s toys

NEVER use apostrophe for plural alone: ‘three dogs’ NOT ‘three dog’s’

💡 Its = possessive (no apostrophe). It’s = it is (apostrophe = contraction).

ENG Q14. What is parallel structure in writing?

Answer:

Items in a list or comparison must use the same grammatical form.

Wrong: She likes running, to swim, and dance.

Right: She likes running, swimming, and dancing.

ACT tests parallel structure in lists, comparisons, and correlative conjunctions.

💡 Watch for: both/and, either/or, neither/nor, not only/but also — all need parallel structure.

ENG Q15. What is the difference between ‘affect’ and ‘effect’?

Answer:

Affect = VERB (to influence)

Example: The weather affected my mood.

Effect = NOUN (the result)

Example: The effect was immediate.

Memory trick: RAVEN — Remember Affect Verb Effect Noun

💡 Rare exceptions: ‘effect’ as verb (to effect change) and ‘affect’ as noun (psychology term).

READ Q16. What is the difference between explicit and implicit information in a passage?

Answer:

Explicit: directly stated in the text — you can point to the exact words.

Implicit: suggested or implied — you must read between the lines.

ACT tests both: detail questions = explicit. Inference questions = implicit.

💡 For implicit questions, the answer must still be supported by evidence in the text.

READ Q17. What is the author’s ‘purpose’ in a passage?

Answer:

Purpose = WHY the author wrote the passage.

Common purposes:

• To inform/explain

• To persuade/argue

• To entertain/narrate

• To describe/analyze

Ask: What does the author want the reader to understand or feel?

💡 Purpose questions often ask about specific paragraphs or details, not just the whole passage.

READ Q18. What is ‘point of view’ in a literary passage?

Answer:

First person: narrator uses ‘I’ — inside the story.

Third person limited: narrator knows one character’s thoughts.

Third person omniscient: narrator knows all characters’ thoughts.

ACT may ask how POV affects meaning or tone.

💡 First person = more personal/subjective. Third person = more distant/objective.

READ Q19. What does ‘connotation’ mean and why does it matter?

Answer:

Connotation = the emotional or cultural associations of a word beyond its literal meaning.

Example: ‘Slim’ vs ‘skinny’ — both mean thin, but ‘slim’ is positive, ‘skinny’ is negative.

ACT vocabulary questions often test connotation in context.

💡 Always ask: does this word have a positive, negative, or neutral connotation in context?

READ Q20. What is a ‘passage structure’ question on the ACT?

Answer:

It asks HOW the passage is organized — the author’s structural strategy.

Common structures:

• Problem → Solution

• Cause → Effect

• Chronological order

• Compare → Contrast

• Claim → Evidence → Conclusion

💡 Read the first and last sentences of each paragraph — they reveal the structure quickly.